Question

1) If we are given a confidence interval, how do we know the margin of error that was used to calculate the confidence interval? You may explain and then provide an example.

2) What is the best way to make a confidence interval more precise, while preserving accuracy? How do we see this in the formula for margin of error?

Answer 1

if the given test is single mean test & confidence interval is given then substract mean from both intervals of confidence interval then we get the margin of error

for example :

consider ,

And , , where n is sample size

95% confidence interval is given for population mean when standard deviation is known

(1.9204,1.9596)

Now as we know the formula of confidence interval,

where , is margin of error

so if we substract From limits of confidence interval then we get margin of error

(1.9204-1.94,1.9596-1.94)

(-0.0196,0.0196)

hence margin of error is

by original formula margin of error is given by

2) These are some best ways ,

1. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...
2. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...
3. Use a one-sided confidence interval. .